The economic impact of Brexit will later be the focus of a debate on common goods while the behind-the-scenes government eyelashes work to gain support for Theresa May.
Ministers will say that this creates a unique partnership with the EU, while Labor argues that it will make people poorer.
On Wednesday, the whip leader, Julian Smith, attempted to win Pro-Brexit-Tories, while officials later informed MEPs of a scenario without agreement.
However, a Brexiter complained that this was an offer for "Spook-Grandees".
Before the third of the five days of the debate, some conservatives suggested that the prime minister postpone the vote next Tuesday to avoid defeat.
A government source told the BBC that whips are testing all options for the majority.
The BBC's political correspondent, Nick Eardley, said there were "fierce speculations about Westminster" about what ministers could offer to get support, including the backlog of MPs and whether the controversial "support" is adopted or not.
However, he added: "From today's point of view, the approval of the Brexit Parliament's approval remains a major challenge".
The Daily Telegraph reports that the EU might be ready to discuss the extension of Article 50 – postponing Brexit to March 29 – if the agreement had been rejected by parliamentarians.
Meanwhile, the Northern Ireland Democratic Union Party, which supports the May administration, said it will support the government in a motion of no confidence if the agreement is removed.
The backstop is designed to protect the peace process of Northern Ireland by preventing the return of customs offices and checkpoints to the Irish border if a future EU-EU trade agreement has not been agreed.
While the whole of the United Kingdom would be temporarily subject to EU customs legislation, it would require new controls on goods transported from Great Britain to Northern Ireland, which the DUP considers unacceptable.
Full legal representation presented to the Council of Ministers before the Brexit agreement was agreed was made public on Wednesday after the government lost an offer of confidentiality.
He revealed the Chief Law Officer's view that support risked a "lengthy negotiation" with the EU could continue "indefinitely" and the UK could not "legally retire" without an EU agreement.
The DUP has said it is "devastating" for Britain.
Jacob Rees-Mogg, president of the European research group Pro-Brexit Conservative Backbench (ERG), met DUP chief Westminster Nigel Dodds on Wednesday.
The press association quoted Rees-Mogg later saying to the ERG that the conservatives risked losing support to the DUP when Ms. May's deal passed, which would have led to the possibility of triggering parliamentary elections .
Parliament could "steal Brexit"
Thursday's debate will be opened by Federal Chancellor Philip Hammond at 11:30 GMT. The Minister of International Trade Liam Fox should close the case after about eight hours.
On Wednesday, Hammond told the Ministry of Commons: "If there is an agreement on the table that will cost very little to the economy, which will allow us to move forward as a nation both economically and politically, I can judge it restrictively, economically this it will be in the best interests of the country. "
Fox warned of the risk that Parliament would try to "steal Brexit from the British people" after parliamentarians decided to comment more on the trial.
He said that there is a "natural majority of Remain" in Parliament, and any attempt to delay the exit of Britain or to reverse the vote in 2016 would be a "democratic affront".